Abstract
In this study, we show that Weyls theorem holds for algebraically class A (s, t) operator acting on Hilbert space. We prove: (i) Weyls theorem holds for f (T) for every f belongs to holomorphic function of spectrum of T; (ii) generalized Weyls theorem holds for T; (iii) the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.
Highlights
Let H be an infinite dimensional Hilbert space and B (H) denote the algebra of all bounded linear operator acting on H
Proof: First we show that if T is class A (s, t) operator, T has SVEP
It can be shown that that Weyl’s theorem holds for algebraically class A(s, t) operator acting on Hilbert
Summary
Let H be an infinite dimensional Hilbert space and B (H) denote the algebra of all bounded linear operator acting on H. Spectral properties of class A (s, t) operators where s, t∈ (0, 1) have been studied by several authors ((Uchiyama and Tanahashi, 2002, Uchiyama et al, 2004). The spectral properties of class A (s, t) operators where s>1, t>1 via their generalized Aluthge transformation and hyponormal transforms has been studied by Stella. Lemma 2: Let T be invertible and quasi nilpotent algebraically class A (s, t) operator.
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